Numerical coherent mode decomposition: validation and applications

Abstract The coherent mode decomposition of the cross-spectral density (CSD) function is a foundational concept in optical coherence theory. While its numerical implementation via matrix diagonalization is a known approach, a rigorous and comprehensive validation of its performance in the scalar regime across diverse physical beam models has been lacking. This paper addresses this gap by presenting the development and validation of a general-purpose numerical engine. To demonstrate its accuracy and versatility, we test the engine against three distinct, analytically tractable cases. Beyond simple validation, we apply the framework to demonstrate two innovative capabilities: first, we showcase its unique diagnostic power to uncover ‘structured coherence’—complex modal content hidden beneath a deceptively simple intensity profile. Second, we validate its application as a powerful metrology tool for the noise-resilient, single-plane calculation of the beam quality factor, M 2 . The performance and numerical limits of this M 2 analysis are characterized via a multi-stage numerical experiment. Furthermore, we demonstrate the framework’s inherent robustness, showing its ability to accurately recover beam properties from data with significant noise. This validated work establishes the direct eigensolution of the CSD as a trusted benchmark and practical tool for analyzing the new classes of data emerging from modern experimental techniques.